{"id":4056,"date":"2022-05-27T09:44:58","date_gmt":"2022-05-27T16:44:58","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=4056"},"modified":"2023-11-09T17:19:24","modified_gmt":"2023-11-10T01:19:24","slug":"algebraic-expressions-lesson-3-episode-5-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/meaning-and-equivalence-of-algebraic-expressions-unit-teachers\/algebraic-expressions-lesson-3-teachers\/algebraic-expressions-lesson-3-episode-5-teachers\/","title":{"rendered":"Algebraic Expressions Lesson 3 Episode 5 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Reflecting<\/h3>\n\n\n\n<div id=\"video_shown_first\" style=\"display:block\">\n<p>\n<div class=\"youtube-player\" data-id=\"BnnatiEEhU8\"><\/div>\n<\/p>\n<p style=\"text-align:center;\"><span style=\"font-size:90%\">No captions <a onclick=\"toggle_text('video_shown_first', 'video_hidden_first')\"><img loading=\"lazy\" decoding=\"async\" width=\"60\" height=\"36\" class=\"wp-image-3255\" style=\"width: 60px;\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2021\/03\/toggle-left.png\" alt=\"toggle left\" srcset=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2021\/03\/toggle-left.png 380w, https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2021\/03\/toggle-left-300x178.png 300w\" sizes=\"auto, (max-width: 60px) 100vw, 60px\" \/><\/a> Captions<\/span><br><span style=\"font-size:80%\"><strong>Stop<\/strong> the video above first if it is playing.<\/span>\n<\/p>\n<\/div>\n<div id=\"video_hidden_first\" style=\"display:none\">\n<p>\n<div class=\"youtube-player\" data-id=\"gf0HdhNzlLA\"><\/div>\n<\/p>\n<p style=\"text-align:center;\"><span style=\"font-size:90%\">No captions <a onclick=\"toggle_text('video_shown_first', 'video_hidden_first')\"><a onclick=\"toggle_text('video_shown_first', 'video_hidden_first')\"><img loading=\"lazy\" decoding=\"async\" width=\"60\" height=\"36\" class=\"wp-image-3256\" style=\"width: 60px;\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2021\/03\/toggle-right.png\" alt=\"toggle right\" srcset=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2021\/03\/toggle-right.png 380w, https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2021\/03\/toggle-right-300x178.png 300w\" sizes=\"auto, (max-width: 60px) 100vw, 60px\" \/><\/a> Captions<\/span><br><span style=\"font-size:80%\"><strong>Stop<\/strong> the video above first if it is playing.<\/span>\n<\/p>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2022\/04\/L3E5_Algebra_Student_Worksheet.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"46\" class=\"wp-image-486\" style=\"width: 150px;\" src=\"http:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/download_worksheets.jpg\" alt=\"Download Math Task\"><\/a> <a rel=\"noreferrer noopener\" href=\"https:\/\/www.online-calculator.com\/\" target=\"_blank\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"48\" class=\"wp-image-485\" style=\"width: 150px;\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/04\/calculator.jpg\" alt=\"Link to on-line calculator\"><\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The students work to explain the relationship between the two algebraic expressions they have written.&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-vivid-cyan-blue-color has-css-opacity has-vivid-cyan-blue-background-color has-background\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Episode Supports<\/h3>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Students\u2019 Conceptual Challenges <input type='hidden' bg_collapse_expand='6a159ecb24cd42010312765' value='6a159ecb24cd42010312765'><input type='hidden' id='bg-show-more-text-6a159ecb24cd42010312765' value=' '><input type='hidden' id='bg-show-less-text-6a159ecb24cd42010312765' value=' '><button id='bg-showmore-action-6a159ecb24cd42010312765' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a159ecb24cd42010312765' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In this episode, ET and Haleemah are asked to use part of each of their two equations, 3c + 2c + 4c = T and (3 + 2 + 4)c = T, to create a new equation. They are not sure what to do\u00a0<strong>[2:37]<\/strong>. Eventually ET writes the equation 9c = T, which was not formed using the other two equations\u00a0<strong>[3:05]<\/strong>. The teacher helps them by selecting 3c + 2c + 4c from one of their equations and 9c from ET\u2019s new equation. She then asks Haleemah and ET whether or not these two expressions are equal. ET thinks they are equal, but his explanation relies only on symbolic reasoning (namely that you add the 3 + 2 + 4 to get 9, and then you put the c back in next to the 9 at the end). Later in the episode, they check the equation 3c + 2c + 4c = 9c by letting c = 5. In Episode 6, Haleemah and ET make sense of the meaning of each part of the equation in the game app context.\u00a0\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Focus Questions <input type='hidden' bg_collapse_expand='6a159ecb24de39074091733' value='6a159ecb24de39074091733'><input type='hidden' id='bg-show-more-text-6a159ecb24de39074091733' value=' '><input type='hidden' id='bg-show-less-text-6a159ecb24de39074091733' value=' '><button id='bg-showmore-action-6a159ecb24de39074091733' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a159ecb24de39074091733' ><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For use in a classroom, pause the video and ask these questions:<\/p>\n\n\n\n<ol class=\"wp-block-list\" style=\"list-style-type:1\">\n<li><strong>[Pause the video at 2:11]<\/strong>\u00a0Ask your students to consider the task in front of Haleemah and ET\u2014how might they combine parts of the equations (3 + 2 + 4)c = T and 3c + 2c + 4c = T to form a new equation that is also true.<\/li>\n\n\n\n<li><strong>[Pause the video at 3:41]<\/strong>\u00a0ET has written a third equation, 9c = T. Ask your students if they can think of any new true equations they could make given this new equation.<\/li>\n\n\n\n<li><strong>[Pause the video at 4:44]<\/strong>\u00a0If you posed Focus Question #2 and your students did not discuss this new equation (3c + 2c + 4c = 9c), ask them if they think this equation is true. Encourage them to explain their reasoning to each other, and then ask for volunteers to explain their reasoning to the class.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\">Supporting Dialogue <input type='hidden' bg_collapse_expand='6a159ecb24f026057595025' value='6a159ecb24f026057595025'><input type='hidden' id='bg-show-more-text-6a159ecb24f026057595025' value=' '><input type='hidden' id='bg-show-less-text-6a159ecb24f026057595025' value=' '><button id='bg-showmore-action-6a159ecb24f026057595025' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-6a159ecb24f026057595025' ><\/p>\n\n\n\n<ol class=\"wp-block-list\" style=\"list-style-type:1\">\n<li>After watching the video, ask your students what they think it means for two equations to be equal. Highlight student ideas about equivalence. Perhaps students say that one side of one equation can be substituted for one side of the other equation and the other equation stays true. Perhaps they mention that both equations work the same way. Encourage them to explain their thinking.<\/li>\n\n\n\n<li>If your students have created their own equations that look different from the ones in the video, you can ask them to display them on whiteboards or through a collaborative app (e.g., see\u00a0<a href=\"http:\/\/www.padlet.com\/\">www.Padlet.com<\/a>). Then ask pairs of students to pick two or three equations and debate whether or not the equations are equivalent. Ask for volunteers to share their partner\u2019s thinking in their own words.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"> <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size wp-block-paragraph\"><\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/meaning-and-equivalence-of-algebraic-expressions-unit-teachers\/algebraic-expressions-lesson-3-teachers\/algebraic-expressions-lesson-3-episode-4-teachers\/\">Previous Episode<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/meaning-and-equivalence-of-algebraic-expressions-unit-teachers\/algebraic-expressions-lesson-3-teachers\/algebraic-expressions-lesson-3-episode-6-teachers\/\">Next Episode<\/a><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/\" style=\"background-color:#2d4059\">Home<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/\" style=\"background-color:#2d4059\">Teachers Home<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/meaning-and-equivalence-of-algebraic-expressions-unit-teachers\/\" style=\"background-color:#2d4059\">AlGeBraiC Expressions<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/meaning-and-equivalence-of-algebraic-expressions-unit-teachers\/algebraic-expressions-lesson-3-teachers\/\" style=\"background-color:#2d4059\">Lesson 3<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Reflecting No captions CaptionsStop the video above first if it is playing. No captions CaptionsStop the video above first if it is playing. The students work to explain the relationship between the two algebraic expressions they have written.&nbsp;&nbsp;&nbsp;&nbsp; Episode Supports Students\u2019 Conceptual Challenges Focus Questions Supporting Dialogue<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":3929,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-4056","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4056","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/comments?post=4056"}],"version-history":[{"count":10,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4056\/revisions"}],"predecessor-version":[{"id":5306,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/4056\/revisions\/5306"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/3929"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=4056"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}